Find vector coordinates with this information?

Question

I have this single linear algebra problem thats struggling me. I have to find the following vector coordinates:

A = λ1E1 + λ2E2 + … + λnEn

With this following information, this is the part I dont understand what does that data represents and how can I get the vector coordinates with it:

If in R':

E1 = (1,0,0,…,0)

E2 = (0,1,0,…,0)

……………………….

En = (0,0,0,…,1)

Can anyone give me a clue of where to start? Thanks.

Answer 1

Simply $A=\begin{pmatrix}\lambda_1\\ \lambda_2\\\vdots\\\lambda_n\end{pmatrix}$.

Answer 2

This is probably a little clearer:

$$ A=\lambda_1 \begin{pmatrix} 1 \\ 0 \\ \vdots \\ 0 \end{pmatrix} +\lambda_2 \begin{pmatrix} 0 \\ 1 \\ \vdots \\ 0 \end{pmatrix} + ... +\lambda_n \begin{pmatrix} 0 \\ 0 \\ \vdots \\ 1 \end{pmatrix} =\begin{pmatrix}\lambda_1\\ \lambda_2\\ \vdots\\ \lambda_n\end{pmatrix} $$

Ced